E2 VoC Analyses Part 2: Regression Analyses

Participant info

Agency task: Agency decisions

Model: Agency decisions by VoC

## Mixed Model Anova Table (Type 3 tests, LRT-method)
## 
## Model: stage_1_choice ~ age_z * voc_z * condition_trial + (voc_z * condition_trial || 
## Model:     subject_id)
## Data: agency_model_data
## Df full model: 12
##                        Effect df      Chisq p.value
## 1                       age_z  1       0.04    .840
## 2                       voc_z  1 168.42 ***   <.001
## 3             condition_trial  1       1.52    .217
## 4                 age_z:voc_z  1  10.92 ***   <.001
## 5       age_z:condition_trial  1       0.14    .712
## 6       voc_z:condition_trial  1  48.77 ***   <.001
## 7 age_z:voc_z:condition_trial  1     5.31 *    .021
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1

## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( logit )
## Formula: stage_1_choice ~ age_z * voc_z * condition_trial + (1 + re1.voc_z +  
##     re1.condition_trial + re1.voc_z_by_condition_trial || subject_id)
##    Data: data
## Control: glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 1e+06))
## 
##      AIC      BIC   logLik deviance df.resid 
##  38178.8  38282.6 -19077.4  38154.8    42082 
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -28.0229  -0.4794   0.2265   0.5457  26.6942 
## 
## Random effects:
##  Groups       Name                         Variance Std.Dev.
##  subject_id   (Intercept)                  2.29016  1.5133  
##  subject_id.1 re1.voc_z                    0.48884  0.6992  
##  subject_id.2 re1.condition_trial          0.64461  0.8029  
##  subject_id.3 re1.voc_z_by_condition_trial 0.05051  0.2247  
## Number of obs: 42094, groups:  subject_id, 135
## 
## Fixed effects:
##                             Estimate Std. Error z value Pr(>|z|)    
## (Intercept)                  0.94898    0.13154   7.214 5.42e-13 ***
## age_z                       -0.02665    0.13149  -0.203 0.839393    
## voc_z                        1.15265    0.06284  18.343  < 2e-16 ***
## condition_trial             -0.08828    0.07109  -1.242 0.214347    
## age_z:voc_z                  0.21148    0.06282   3.366 0.000762 ***
## age_z:condition_trial       -0.02626    0.07109  -0.369 0.711856    
## voc_z:condition_trial        0.19899    0.02570   7.744 9.63e-15 ***
## age_z:voc_z:condition_trial  0.05987    0.02574   2.326 0.020032 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) age_z  voc_z  cndtn_ ag_z:v_ ag_z:c_ vc_z:_
## age_z        0.001                                            
## voc_z        0.010  0.001                                     
## conditn_trl  0.006 -0.002  0.002                              
## age_z:voc_z  0.001  0.009  0.007  0.000                       
## ag_z:cndtn_ -0.003  0.002  0.000 -0.001  0.001                
## vc_z:cndtn_  0.003  0.000  0.029  0.030 -0.001   0.004        
## ag_z:vc_z:_  0.000  0.001  0.001  0.004  0.023   0.030   0.024

Plot: Sensitivity to the value of choice

Plot: Sensitivity to value of choice with continuous age

Summary stats: Sensitivity to value of control

Agency task: Machine selection

Model: Optimal machine choices across trials by condition and age

## Mixed Model Anova Table (Type 3 tests, LRT-method)
## 
## Model: stage_2_acc ~ age_z * context * condition_trial + (context * 
## Model:     condition_trial || subject_id)
## Data: machine_model_data
## Df full model: 12
##                          Effect df     Chisq p.value
## 1                         age_z  1 18.88 ***   <.001
## 2                       context  1 25.05 ***   <.001
## 3               condition_trial  1 66.49 ***   <.001
## 4                 age_z:context  1      0.26    .612
## 5         age_z:condition_trial  1      1.22    .268
## 6       context:condition_trial  1    3.44 +    .064
## 7 age_z:context:condition_trial  1      1.99    .159
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1

## Generalized linear mixed model fit by maximum likelihood (Laplace
##   Approximation) [glmerMod]
##  Family: binomial  ( logit )
## Formula: stage_2_acc ~ age_z * context * condition_trial + (1 + re1.context1 +  
##     re1.condition_trial + re1.context1_by_condition_trial ||      subject_id)
##    Data: data
## Control: glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 1e+06))
## 
##      AIC      BIC   logLik deviance df.resid 
##  13066.7  13160.8  -6521.4  13042.7    18640 
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -11.0512   0.0954   0.2009   0.3937   2.4327 
## 
## Random effects:
##  Groups       Name                            Variance Std.Dev.
##  subject_id   (Intercept)                     1.7436   1.3205  
##  subject_id.1 re1.context1                    0.5702   0.7551  
##  subject_id.2 re1.condition_trial             0.3025   0.5500  
##  subject_id.3 re1.context1_by_condition_trial 0.1182   0.3439  
## Number of obs: 18652, groups:  subject_id, 135
## 
## Fixed effects:
##                                Estimate Std. Error z value Pr(>|z|)    
## (Intercept)                     2.32963    0.12060  19.317  < 2e-16 ***
## age_z                           0.53498    0.11947   4.478 7.54e-06 ***
## context1                        0.38956    0.07338   5.309 1.10e-07 ***
## condition_trial                 0.52529    0.05755   9.128  < 2e-16 ***
## age_z:context1                 -0.03839    0.07341  -0.523   0.6010    
## age_z:condition_trial           0.06404    0.05722   1.119   0.2631    
## context1:condition_trial        0.08002    0.04225   1.894   0.0582 .  
## age_z:context1:condition_trial -0.06096    0.04231  -1.441   0.1497    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) age_z  cntxt1 cndtn_ ag_z:1 ag_z:_ cnt1:_
## age_z        0.049                                          
## context1     0.032  0.007                                   
## conditn_trl  0.080  0.016  0.027                            
## ag_z:cntxt1  0.004  0.023  0.073 -0.001                     
## ag_z:cndtn_  0.011  0.065 -0.001  0.089  0.020              
## cntxt1:cnd_  0.023  0.001  0.113  0.070  0.024  0.012       
## ag_z:cnt1:_ -0.003  0.016  0.022  0.011  0.116  0.062  0.135

Plot: Proportion optimal machine selections across age groups and trials

Explicit reward knowledge task

Explicit reward knowledge task: summary stats

Model: Explicit reward knowledge by age and true probabilities

## Mixed Model Anova Table (Type 3 tests, S-method)
## 
## Model: error ~ zTrueProb * zAge + (1 | subject_id)
## Data: explicitKnow.filtered
##           Effect        df         F p.value
## 1      zTrueProb 1, 673.00 22.78 ***   <.001
## 2           zAge 1, 133.00   7.01 **    .009
## 3 zTrueProb:zAge 1, 673.00      0.26    .609
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1

## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: error ~ zTrueProb * zAge + (1 | subject_id)
##    Data: data
## 
## REML criterion at convergence: 2763.4
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -1.5472 -0.7030 -0.1787  0.4401  4.2139 
## 
## Random effects:
##  Groups     Name        Variance Std.Dev.
##  subject_id (Intercept) 0.1176   0.3429  
##  Residual               1.6465   1.2831  
## Number of obs: 810, groups:  subject_id, 135
## 
## Fixed effects:
##                 Estimate Std. Error        df t value Pr(>|t|)    
## (Intercept)      1.56296    0.05389 133.00000  29.005  < 2e-16 ***
## zTrueProb       -0.21530    0.04511 673.00000  -4.772 2.23e-06 ***
## zAge            -0.14272    0.05392 133.00000  -2.647  0.00911 ** 
## zTrueProb:zAge  -0.02307    0.04514 673.00000  -0.511  0.60947    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Correlation of Fixed Effects:
##             (Intr) zTrPrb zAge 
## zTrueProb   0.000              
## zAge        0.000  0.000       
## zTruPrb:zAg 0.000  0.000  0.000

Plot: Explicit reward knowledge